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October, 1986 A Sufficient Condition for Association of a Renewal Process
Robert M. Burton Jr., Ed Waymire
Ann. Probab. 14(4): 1272-1276 (October, 1986). DOI: 10.1214/aop/1176992368

Abstract

Let $\{N(t): t \geq 0\}$ be a renewal counting process with lifetime density $f(t)$. For each bounded Borel set $A$ contained in $\lbrack 0, \infty)$, denote the number of renewals in $A$ by $N(A)$. The renewal process is called associated if the corresponding family of random variables, $N(A)$, is associated. The result of this note is that the renewal process is associated whenever $\log(f)$ is a convex function (which implies a decreasing failure rate).

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Robert M. Burton Jr.. Ed Waymire. "A Sufficient Condition for Association of a Renewal Process." Ann. Probab. 14 (4) 1272 - 1276, October, 1986. https://doi.org/10.1214/aop/1176992368

Information

Published: October, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0608.60084
MathSciNet: MR866348
Digital Object Identifier: 10.1214/aop/1176992368

Subjects:
Primary: 60K05
Secondary: 60K10

Keywords: association , Renewal process

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • October, 1986
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